Direct Numerical Simulation of expansion, hydrodynamic mixing, and heat transfer to electrodes during low-temperature plasma discharges in atmospheric air*

Low-temperature non-equilibrium plasmas have garnered significant interest from various communities. Nanosecond Pulsed Discharges (NSPD) in a pin-to-pin configuration are an efficient manner of generating such plasmas in ignition and flow control applications. However, the broad range of time and length scales involved in modelling NSPD configurations present formidable challenges to existing solvers. These challenges have led to the study of NSPDs in simplified conditions such as 0-D kinetics studies, the early discharge phase, or neglecting plasma processes altogether. In previous work, we presented a comprehensive solver that incorporates electrostatic processes, plasma relevant species, and the reactive Navier-Stokes equations in a fully-coupled manner. In this work, we use the solver to simulate a three-dimensional pin-to-pin NSPD in quiescent air at atmospheric conditions for several hundred microseconds. The asymmetric streamer propagation leads to the formation of a pressurized channel with two distinct temperature kernels near the electrodes. The pressurized channel relaxation results in complex shock dynamics for the following few microseconds, which is then followed by cool gas entrainment towards the middle of the gap. The metal electrode plays a prominent role both as a source of vorticity and heat transfer throughout the process. The observed phenomena are highly relevant to the induced hydrodynamics and mixing in the discharge channel, affecting subsequent pulses.